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We shall prove that the celebrated R\'enyi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the $Z$-entropies. Each of them, under suitable hypotheses, generalizes the celebrated…
Certifying individual quantum devices with minimal assumptions is crucial for the development of quantum technologies. Here, we investigate how to leverage single-system contextuality to realize self-testing. We develop a robust…
In device-independent (DI) quantum protocols, the security statements are oblivious to the characterization of the quantum apparatus - they are based solely on the classical interaction with the quantum devices as well as some well-defined…
In an empirical logic, an experimentally verifiable proposition P relating to a quantum system is assigned the value of either true of false if the system is in the pure state that belongs or, respectively, does not belong to the Hilbert…
Differential privacy (DP) provides a mathematical guarantee limiting what an adversary can learn about any individual from released data. However, achieving this protection typically requires adding noise, and noise can accumulate when many…
We construct here an iterative evaluation of all PR map codes: progress of this iteration is measured by descending complexity within "Ordinal" O := N[\omega] of polynomials in one indeterminate, ordered lexicographically. Non-infinit…
Non-stabilizerness is an essential resource for quantum computational advantage, as stabilizer states admit efficient classical simulation. We develop a semi-device-independent framework for certifying non-stabilizer states in…
We first prove that ontological models of the quantum state which are capable of reproducing the Born probability rule and fall in the class of $\psi$-epistemic models are inconsistent with the Sch{\"o}dinger time evolution. We then model…
Rice's Theorem states that every nontrivial language property of the recursively enumerable sets is undecidable. Borchert and Stephan initiated the search for complexity-theoretic analogs of Rice's Theorem. In particular, they proved that…
Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations, and plays an important role in device-independent quantum information processing as well as quantum complexity…
A remarkable feature of quantum theory is that particles with identical intrinsic properties must be treated as indistinguishable if the theory is to give valid predictions. In the quantum formalism, indistinguishability is expressed via…
Self-testing--the attractive possibility to infer the underlying physics of a quantum device in a black-box scenario--has gained increased traction in recent years, with applications to device-independent quantum information processing.…
We analyze the recent no go theorem by Pusey, Barrett and Rudolph (PBR) concerning ontic and epistemic hidden variables. We define two fundamental requirements for the validity of the result. We finally compare the models satisfying the…
Beklemishev introduced an ordinal notation system for the Feferman-Sch\"utte ordinal $\Gamma_0$ based on the autonomous expansion of provability algebras. In this paper we present the logic $\textbf{BC}$ (for Bracket Calculus). The language…
The existence of pseudorandom unitaries (PRUs) -- efficient quantum circuits that are computationally indistinguishable from Haar-random unitaries -- has been a central open question, with significant implications for cryptography,…
The Free Energy Principle (FEP) states that under suitable conditions of weak coupling, random dynamical systems with sufficient degrees of freedom will behave so as to minimize an upper bound, formalized as a variational free energy, on…
We derive a systematic approach to the thermodynamics of quantum systems based on the underlying symmetry groups. We show that the entropy of a system can be described in terms of group-theoretical quantities that are largely independent of…
Upon reading Einstein's views on quantum incompleteness in publications or in his correspondence after 1935 (the EPR paradox), one gets a very intense feeling of deja-vu. Einstein presents a quantum hole argument, which somewhat reminds of…
Reliable experimental demonstrations of violations of local realism are highly desirable for fundamental tests of quantum mechanics. One can quantify the violation witnessed by an experiment in terms of a statistical p-value, which can be…
Retrieving classical information from quantum systems is central to quantum information processing. As a more general task than quantum state discrimination, which focuses on identifying the exact state, quantum state exclusion only…